Evaluate the definite integral. $\int^{1}_{9}\left(-15\sqrt{x}\right)\,dx = $
Explanation: First, use the power rule: $\begin{aligned}\int^{1}_{9}\left(-15\sqrt{x}\right)\,dx ~&=~\int^{1}_{9}\left(-15x^{\frac12}\right)\,dx \\&=(-10x^\frac32)\Bigg|^{1}_{{9}}\end{aligned}$ Second, plug in the limits of integration: $(-10\cdot{1}^{\frac32})-(-10\cdot{9}^{\frac32}) = -10+270 = 260$. The answer: $\int^{1}_{9}\left(-15\sqrt{x}\right)\,dx ~=~260$